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Chapter 7: Q. 12 (page 500)

Express the product $\sin 4 θ \cos 6 θ$ as a sum containing only sines or only cosines.

Short Answer

Expert verified

$\sin 4 θ \cos 6 θ = \frac{\sin (10 θ) - \sin (2 θ)}{2}$

Step by step solution

01

Step 1. Given expression

$\sin 4 θ \cos 6 θ$

02

Step 2. Rewriting the expression

$2 \sin A \cos B = \sin (A + B) + \sin (A - B) s o, \sin 4 θ \cos 6 θ = \frac{\sin (10 θ) + \sin (- 2 θ)}{2} = \frac{\sin (10 θ) - \sin (2 θ)}{2} (\sin (- θ) = - \sin θ$

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Most popular questions from this chapter

True or False: $\tan (θ) \cos (θ) = \sin (θ)$ for any $θ \neq \frac{(2 k + 1) π}{2}$

Multiply: $\frac{\cos (θ)}{1 - \sin (θ)} \frac{1 + \sin (θ)}{1 + \sin (θ)}$

If $x = 2 \tan θ$ , express $\sin (2 θ)$ as a function ofx.

In Problems 9–36, find the exact value of each expression.

$\cos [\sin^{- 1} (- \frac{\sqrt{3}}{2})]$

In Problems 9–36, find the exact value of each expression.

$\cos (\sin^{- 1} \frac{\sqrt{2}}{2})$

See all solutions

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